Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-06-21T03:25:39.094Z Has data issue: false hasContentIssue false

8 - Diffusion

Published online by Cambridge University Press:  30 November 2023

Nikolai Kocherginsky
Affiliation:
University of Illinois, Urbana-Champaign
Get access

Summary

Based on physicochemical mechanics, Chapter 8 discusses complicated problems of multicomponent and thermodiffusion, and gives the generalizedFick’s law and generalized Onsagedr’s reciprocal relations.

Type
Chapter
Information
Physicochemical Mechanics
With Applications in Physics, Chemistry, Membranology and Biology
, pp. 188 - 240
Publisher: Cambridge University Press
Print publication year: 2023

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Agar, J. N., Mou, C. & Lin, J.-I., 1989. Single-ion heat of transport in electrolyte solutions: A hydrodynamic theory. Journal of Physical Chemistry, 93, pp. 20792082.CrossRefGoogle Scholar
Annunziata, O., Buzatu, D. & Albright, J. G., 2012. Protein diffusiophoresis and salt osmotic diffusion in aqueous solutions. Journal of Physical Chemistry B, 116, pp. 1269412705.CrossRefGoogle ScholarPubMed
Astumian, R. D., 2007. Coupled transport at the nanoscale: The unreasonable effectiveness of equilibrium theory. Proceedings of the National Academy of Sciences of the United States of America, 104(1), pp. 34.CrossRefGoogle ScholarPubMed
Atkins, P. & de Paula, J., 2002. Atkins’ Physical Chemistry. 7th ed. Oxford: Oxford University Press.Google Scholar
Barros, M. C. F., Ribeiro, A.C.F., Esteso, M.A., Lobo, V.M.M., Leaist, D.G., 2014. Diffusion of levodopa in aqueous solutions of hydrochloric acid at 25 °C. Journal of Chemical Thermodynamics, 72, pp. 4447.CrossRefGoogle Scholar
Burelbach, J., Frenkel, D., Pagonabarraga, I. & Eiser, E., 2018. A unified description of colloidal thermophoresis. European Physical Journal E, 41(7), pp. 112.CrossRefGoogle ScholarPubMed
Calvo, I., Sánchez, Carreras, R., B. A., and. van Milligen, B. Ph, 2007. Fractional generalization of Fick’s law: A microscopic approach. Physical Review Letters, 99, 230603.CrossRefGoogle Scholar
Chakraborty, B., Wang, J. & Eapen, J., 2013. Multicomponent diffusion in molten LiCl-KCl: Dynamical correlations and divergent Maxwell-Stefan diffusivities. Physical Review E, 87, 052312.CrossRefGoogle ScholarPubMed
Chemla, M. & Okada, I., 1990. Ionic mobilities of monovalent cations in molten-salt mixtures. Electrochimica Acta, 35, pp. 17611776.CrossRefGoogle Scholar
Chen, T., Dave, K. & Gruebele, M., 2018. Pressure‐ and heat‐induced protein unfolding in bacterial cells: Crowding vs. sticking. FEBS Letters, 592, pp. 13571365.CrossRefGoogle ScholarPubMed
Chevalier, C., Debbasch, F. & Rivet, J., 2009. Stochastic models of thermodiffusion. Modern Physics Letters B, 23(9), pp. 11471155.CrossRefGoogle Scholar
Crank, J., 1975. The Mathematics of Diffusion. 2nd ed. Oxford: Oxford University Press.Google Scholar
Cussler, E. L., 1997. Diffusion: Mass Transfer in Fluid Systems. 2nd ed. Cambridge: Cambridge University Press.Google Scholar
Darken, L., 1948. Diffusion, mobility and their interrelation through free energy in binary metallic systems. Transactions AIME, 175, pp. 184201.Google Scholar
de Groot, S. R. & Mazur, P., 1962. Non-equilibrium Thermodynamics. Amsterdam: North-Holland.Google Scholar
Dhont, J., 2004. Thermodiffusion of interacting colloids. I: A statistical thermodynamics approach. Journal of Chemical Physics, 120(3), pp. 16321641.CrossRefGoogle Scholar
Di Lecce, S., Albrechta, T. & Bresme, F., 2017. The role of ion–water interactions in determining the Soret coefficient of LiCl aqueous solutions. Physical Chemistry Chemical Physics, 19, pp. 95759583.CrossRefGoogle ScholarPubMed
Duhr, S. & Braun, D., 2006. Why molecules move along a temperature gradient. Proceedings of the National Academy of Sciences of the United States of America, 103(52), pp.1967819682.CrossRefGoogle ScholarPubMed
Einstein, A., 1956. Investigations on the Theory of the Brownian Movement. New York: Dover.Google Scholar
Eslamian, M., 2011. Advances in thermodiffusion and thermophoresis (Soret effect) in liquid mixtures. Frontiers in Heat and Mass transfer, 2, 043001.Google Scholar
Eslamian, M. & Saghir, M. Z., 2012. Thermodiffusion applications in MEMS, NEMS and solar cell fabrication by thermal metal doping of semiconductors. Fluid Dynamics & Material Processing, 8(4), pp. 353380.Google Scholar
Fick, A., 1855. Ueber diffusion. Annalen der Physik, 94, pp. 5986.CrossRefGoogle Scholar
Gorban, A. N., Sargsyan, H. P. & Wahab, H. A., 2011. Quasichemical models of multicomponent nonlinear diffusion. Mathematical Modelling of Natural Phenomena, 6, pp. 184262.CrossRefGoogle Scholar
Greenwood, D. T., 1977. Classical Dynamics. Mineola: Dover.Google Scholar
Haase, R., 1969. Thermodynamics of Irreversible Processes. Reading: Addison-Wesley.Google Scholar
Hepler, L. & Hovey, J., 1996. Standard state heat capacities of aqueous electrolytes and some related undissociated species. Canadian Journal of Chemistry, 74, pp. 639649.CrossRefGoogle Scholar
Hu, B., Hnedkovsky, L. & Hefter, G., 2016. Heat capacities of aqueous solutions of lithium sulfate, lithium perchlorate, and lithium trifluoromethanesulfomate at 298.15 K. Journal of Chemical and Engineering Data, 61, pp. 21492154.CrossRefGoogle Scholar
Hunter, R. J., 1995. Foundations of Colloid Science. Vol. 1. Oxford: Clarendon Press.Google Scholar
Islam, M., 2004. Fickian diffusion equation: An unsolved problem. Physica Scripta, 70, pp. 114119.CrossRefGoogle Scholar
Jakupi, P., Halvorsen, H. & Leaist, D. G., 2004. A thermodynamic interpretation of the “excluded-volume effect” in coupled diffusion. Journal of Physical Chemistry B, 108, pp. 79787985.CrossRefGoogle Scholar
Kianinia, Y., Hnedkovsky, L., Senanayake, G., Akilan, C., Khalesi, M. R., Abdollahy, M., 2018. Heat capacities of aqueous solutions of K4Fe(CN)6, K3Fe(CN)6, K3Co(CN)6, K2Ni(CN)4, and KAg(CN)2 at 298.15 K. Journal of Chemical and Engineering Data, 63, pp. 17731779.CrossRefGoogle Scholar
Kincaid, J., Eyring, H. & Stern, A., 1941. The theory of absolute reaction rates and its application to viscosity and diffusion in the liquid state. Chemical Reviews, 28, pp. 301365.CrossRefGoogle Scholar
Kocherginsky, N. M., 2010. Mass transport and membrane separations: Universal description in terms of physicochemical potential and Einstein’s mobility. Chemical Engineering Science, 65, pp. 14741489.CrossRefGoogle Scholar
Kocherginsky, N. M. & Gruebele, M., 2013. A thermodynamic derivation of the reciprocal relations. Journal of Chemical Physics, 138(12), 124502.CrossRefGoogle ScholarPubMed
Kocherginsky, N. M. & Gruebele, M., 2016. Mechanical approach to chemical transport. Proceedings of the National Academy of Sciences of the United States of America, 113(40), pp. 1111611121.CrossRefGoogle ScholarPubMed
Kocherginsky, N. M. & Gruebele, M., 2021. Thermodiffusion: The physico-chemical mechanics view. Journal of Chemical Physics, 154, 024112.CrossRefGoogle ScholarPubMed
Kocherginsky, N. M. & Qian, Y., 2007. Big Carrousel mechanism of copper removal from ammoniacal wastewater through supported liquid membrane. Separation and Purification Technology, 54, pp. 104116.CrossRefGoogle Scholar
Kocherginsky, N. M. & Stucki, J. W., 2000. Process for removal of Strontium ions from strong alkaline solutions. Singapore Patent No. #70059.Google Scholar
Kocherginsky, N. M. & Wang, Z., 2008. Ion/electron coupled transport through polyaniline membrane: Fast transmembrane redox reactions at neutral pH. Journal of Physical Chemistry B, 112, pp. 70167021.CrossRefGoogle ScholarPubMed
Kocherginsky, N. M. & Zhang, Y. K., 2003. Role of standard chemical potential in transport through anisotropic media and asymmetrical membranes. Journal of Physical Chemistry B, 107, pp. 78307837.CrossRefGoogle Scholar
Kondepudi, D. & Prigogine, I., 1998. Modern Thermodynamics: From Heat Engines to Dissipative Structures. Chichester: John Wiley.Google Scholar
Krishna, R. & Wesselingh, J. A., 1997. The Maxwell-Stefan approach to mass transfer. Chemical Engineering Science, 52, pp. 861911.CrossRefGoogle Scholar
Lakshminarayanaiah, N., 1969. Transport Phenomena in Membranes. New York: Academic Press.Google Scholar
Landau, L. D. & Lifshitz, E. M., 1987. Fluid Mechanics: Course of Theoretical Physics. Vol. 6. 2nd ed. Amsterdam: Elsevier.Google Scholar
Leaist, D. G. & Hao, L., 1993. Diffusion in buffered protein solutions: Combined Nernst-Planck and multicomponent Fick equations. Journal of the Chemical Society, Faraday Transactions, 89, pp. 27752782.CrossRefGoogle Scholar
Leonardi, E., D’Aguanno, B. & Angeli, C., 2008. Influence of the interaction potential and of the temperature on the thermodiffusion (Soret) coefficient in a model system. Journal of Chemical Physics, 128(054507), pp. 112.CrossRefGoogle ScholarPubMed
Likhtenshtein, G., 2016. Electron Spin Interactions in Chemistry and Biology: Fundamentals, Methods, Reactions Mechanisms, Magnetic Phenomena, Structure Investigation. Switzerland: Springer International.Google Scholar
March, N. H. & Tosi, M. P., 2002. Introduction to Liquid State Physics. Singapore: World Scientific.CrossRefGoogle Scholar
Marcus, Y. & Loewenschuss, A., 1984. Standard entropies of hydration of ions. Annual Reports Progress of Chemistry. Section C: Physical Chemistry, 81, pp. 81135.CrossRefGoogle Scholar
Maxwell, J., 1952. On the Dynamical Theory of Gases. Scientific Papers. New York: Dover.Google Scholar
Miller, D. G., 1960. Thermodynamics of irreversible processes: The experimental verification of the Onsager reciprocal relations. Chemical Reviews, 60, pp. 1537.CrossRefGoogle Scholar
Miller, D. G., Vitagliano, V. & Sartorio, R., 1986. Some comments on multicomponent diffusion: Negative main term diffusion-coefficients, second law constraints, solvent choices, and reference frame transformations. Journal of Physical Chemistry, 90, pp. 15091519.CrossRefGoogle Scholar
Monroe, C. W., Wheeler, D. R. & Newman, J., 2015. Nonequilibrium linear response theory: Application to Onsager-Stefan-Maxwell diffusion. Industrial & Engineering Chemistry Research, 54, pp. 44604467.CrossRefGoogle Scholar
Morgan, B. & Madden, P., 2004. Ion mobilities and microscopic dynamics in liquid (Li,K)Cl. Journal of Chemical Physics, 120, pp. 14021413.CrossRefGoogle ScholarPubMed
Morgan, K., Maguire, N., Fushimi, R., Gleaves, J. T., Kondratenko, E. V., Yablonsky, G. S., 2017. Forty years of temporal analysis of products. Catalysis Science and Technology, 7, pp. 24162439.CrossRefGoogle Scholar
Nair, R., Wu, H. A., Jayaram, P.N., Grigorieva, I. V., Geim, A. K., 2012. Unimpeded permeation of water through helium-leak-tight graphene-based membranes. Science, 335(6067), pp. 442444.CrossRefGoogle ScholarPubMed
Nicholls, D. G. & Ferguson, S. J., 1992. Bioenergetics 2. San Diego: Academic Press.Google Scholar
Niether, D. & Wiegand, S., 2019. Thermophoresis of biological and biocompatible compounds in aqueous solution. Journal of Physics: Condensed Matter, 31, 503003.Google ScholarPubMed
Okada, I., 1999. The Chemla effect: From the separation of isotopes to the modeling of binary ionic liquids. Journal of Molecular Liquids, 83, pp. 522.CrossRefGoogle Scholar
Onsager, L., 1931. Reciprocal relations in irreversible processes. II. Physical Review, 38(12), pp. 22652279.CrossRefGoogle Scholar
Onsager, L., 1945. Theories and problems of liquid diffusion. Annals of the New York Academy of Sciences, 46, pp. 241265.CrossRefGoogle ScholarPubMed
Polson, N. & Roberts, G., 1994. Bayes factors for discrete observations from diffusion processes. Biometrika, 81, pp. 1126.CrossRefGoogle Scholar
Prigogine, I., 1961. Introduction to Thermodynamics of Irreversible Processes. 2nd ed. New York: John Wiley.Google Scholar
Prigogine, I. & Defay, R., 1954. Chemical Thermodynamics. London: Longmans.Google Scholar
Rard, J. A., Albright, J. G. & Miller, D. G., 2009. Diffusion Onsager coefficients Lij for the NaCl + Na2SO4 + H2O system at 298.15 K. Journal of Chemical and Engineering Data, 54, pp. 636651.CrossRefGoogle Scholar
Risken, H., 1989. The Fokker-Planck Equation, Methods of Solution and Applications. 2nd ed. Berlin: Springer.Google Scholar
Roos, N., 2014. Entropic forces in Brownian motion. American Journal of Physics, 82(12), pp. 11611166.CrossRefGoogle Scholar
Safran, S., 1994. Statistical Thermodynamics of Surfaces, Interfaces, and Membranes. Reading: Addison-Wesley.Google Scholar
Salez, T., Nakamae, S., Perzynski, R., Roger, M. 2018. Thermoelectricity and thermodiffusion in magnetic nanofluids: Entropic analysis. Entropy, 20(405), pp. 127.CrossRefGoogle ScholarPubMed
Sattin, F., 2008. Fick’s law and Fokker-Planck equation in inhomogeneous environments. Physics Letters A, 372, pp. 39413945.CrossRefGoogle Scholar
Schmidt-Nielsen, K., 1997. Animal Physiology: Adaptation and Environment. 5th ed. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Smith, R. C. & Grandy, W. T., 1985. Maximum-Entropy and Bayesian Methods in Inverse Problems. Dordrecht: Kluwer Academic.CrossRefGoogle Scholar
Stefan, J., 1871. Über das Gleichgewicht und Bewegung, insbesondere die Diffusion von Gemischen. Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften Wien, 2te Abteilung a, 63, pp. 63124.Google Scholar
Tan, C., Albright, J. G. & Annunziata, O., 2008. Determination of preferential interaction parameters by multicomponent diffusion: Applications to poly(ethylene glycol)-salt-water ternary mixtures. Journal of Physical Chemistry B, 112, pp. 49674974.CrossRefGoogle ScholarPubMed
Taylor, R. & Krishna, R., 1993. Multicomponent Mass Transfer. New York: Wiley.Google Scholar
Teorell, T., 1935. Studies on the “diffusion effect” upon ionic distribution I: Some theoretical considerations. Proceedings of the National Academy of Sciences of the United States of America, 21, pp. 152161.CrossRefGoogle ScholarPubMed
Truesdell, C., 1962. Mechanical basis of diffusion. Journal of Chemical Physics, 37, pp. 23362344.CrossRefGoogle Scholar
Tyrrell, H. J. V., 1961. Diffusion and Heat Flow in Liquids. London: Butterworths.Google Scholar
van Kampen, N. G., 1988. Diffusion in inhomogeneous media. Journal of Physics and Chemistry of Solids, 49(6), pp. 673677.CrossRefGoogle Scholar
van Milligen, B. P., Carreras, B. A. & Sánchez, R., 2005. The foundations of diffusion revisited. Plasma Physics and Controlled Fusion, 47, pp. B743B754.CrossRefGoogle Scholar
Verlinde, E., 2011. On the origin of gravity and the laws of Newton. Journal of High Energy Physics. https://doi.org/10.1007/JHEP04(2011)029.CrossRefGoogle Scholar
Yablonsky, G. S., Constales, D. V., Galvita, V. & Marin, G. B., 2011. Reciprocal relations between kinetic curves. Europhysics Letters, 93(2), 20004.CrossRefGoogle Scholar
Yang, M. & Ripoll, M., 2013. Brownian motion in inhomogeneous suspensions. Physical Review E, 87, 062110.CrossRefGoogle ScholarPubMed
Zwanzig, R., 1988. Diffusion in a rough potential. Proceedings of the National Academy of Sciences of the United States of America, 85, pp. 20292030.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Diffusion
  • Nikolai Kocherginsky, University of Illinois, Urbana-Champaign
  • Book: Physicochemical Mechanics
  • Online publication: 30 November 2023
  • Chapter DOI: https://doi.org/10.1017/9781108368629.009
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Diffusion
  • Nikolai Kocherginsky, University of Illinois, Urbana-Champaign
  • Book: Physicochemical Mechanics
  • Online publication: 30 November 2023
  • Chapter DOI: https://doi.org/10.1017/9781108368629.009
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Diffusion
  • Nikolai Kocherginsky, University of Illinois, Urbana-Champaign
  • Book: Physicochemical Mechanics
  • Online publication: 30 November 2023
  • Chapter DOI: https://doi.org/10.1017/9781108368629.009
Available formats
×